Solving System of Linear Equations Using Inverse

Q. The condition for which the equations 2x – 3y = 4, 5x – ky = 5 are consistent with unique solution is

Q.

Which of the following options holds true for the system of equations,

x + y + z =6

x + 2y + 3z = 12

x + 4y + 7z =30

1. No solution

2. Infinite solution

3. Unique Non trivial solutions

4. Trivial solution only

Q. The system of equations x + ky + 3z = 0, 3x + ky - 2z = 0, 2x + 3y - 4z = 0 possess a non-trivial solution over the set of rationals, then 2k is an integral element of the interval

1. [10, 20]
2. (20, 30)
3. [30, 40]
4. (40, 50)

Q. for which value of k , the system of equation (k+2)x+4y+8=0 and (7-k)x+6y-5=0 does not have a unique solution

Q.

The given set of equations has at least one non trivial solution.

x + 3y + 2z =0

2x + y + 4z = 0

x + 11y + 14z =0

1. True

2. False

Q. If $p\left(x\right)=x^2-4x+3$, then the value of $p\left(2\right)+p\left(1\right)$ is.

1. $-1$
2. $0$
3. $-3$

Q.

For each of the following system of equations find whether it has unique solution, infinite number of solutions or no solutions.

$x+2y=1,2x-3y=12$

Q. If $p\left(x\right)=x^2-4x+3$, then the value of $p\left(2\right)+p\left(1\right)$ is.

1. $-1$
2. $0$
3. $-3$

Q.

Give the equations of two lines passing through (2, 14). How many more such lines are there, and why?

Q.

Verify whether the line 3x + 4y = 7 passes through the point (1, 1)

Q. If $p\left(x\right)=x^2+5x+9$, then the value of \(p(3)\ is .

Q. { †ext { The system of equations } 2 x - a y = 4 ; 5 x - k y = 5 †ext { is in consistant with no unique } } { †ext { solution. If } k †ext { and a are natural numbers, then the minimum possible value of } ( a + k ) } { †ext { is equal to }

Q. If $p\left(x\right)=x^2+5x+9$, then the value of \(p(3)\ is .

Q.

Give the equations of two lines passing through (2, 14). How many more such lines are there, and why?

Q.

An exactly determined system always has solutions.

1. True

2. False

Q. Find the value of $c$ for which the pair of equations $cx-y=2$ and $6x-2y=3$ will have infinitely many solutions.

Q.

What is the graph of a linear equation in 2 variables?

1. None of these

2. Sine wave

3. Parabola

4. Straight line